Quantile Markov Decision Processes

The goal of a traditional Markov decision process (MDP) is to maximize expected cumulative reward over a defined horizon (possibly infinite). In many applications, however, a decision maker may be interested in optimizing a specific quantile of the cumulative reward instead of its expectation. In th...

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Bibliographic Details
Published in:Operations research Vol. 70; no. 3; p. 1428
Main Authors: Li, Xiaocheng, Zhong, Huaiyang, Brandeau, Margaret L
Format: Journal Article
Language:English
Published: United States 01.05.2022
Subjects:
Markov Decision Process
Dynamic Programming
Risk Measure
Quantile
Medical Decision Making
ISSN:0030-364X
Online Access:Get more information
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Summary:The goal of a traditional Markov decision process (MDP) is to maximize expected cumulative reward over a defined horizon (possibly infinite). In many applications, however, a decision maker may be interested in optimizing a specific quantile of the cumulative reward instead of its expectation. In this paper we consider the problem of optimizing the quantiles of the cumulative rewards of a Markov decision process (MDP), which we refer to as a quantile Markov decision process (QMDP). We provide analytical results characterizing the optimal QMDP value function and present a dynamic programming-based algorithm to solve for the optimal policy. The algorithm also extends to the MDP problem with a conditional value-at-risk (CVaR) objective. We illustrate the practical relevance of our model by evaluating it on an HIV treatment initiation problem, where patients aim to balance the potential benefits and risks of the treatment.
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ISSN:0030-364X
DOI:10.1287/opre.2021.2123